CHAJDA, Ivan, Helmut LANGER a Jan PASEKA. Algebraic Aspects of Relatively Pseudocomplemented Posets. Order-A Journal on the Theory of Ordered Sets and its Applications. Dordrecht: Springer, 2020, roč. 37, č. 1, s. 1-29. ISSN 0167-8094. Dostupné z: https://dx.doi.org/10.1007/s11083-019-09488-1. |
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@article{1693381, author = {Chajda, Ivan and Langer, Helmut and Paseka, Jan}, article_location = {Dordrecht}, article_number = {1}, doi = {http://dx.doi.org/10.1007/s11083-019-09488-1}, keywords = {Relative pseudocomplementation; Poset; Hilbert algebra; Congruence; Convex poset; Dedekind-MacNeille completion; Glivenko equivalence; Category}, language = {eng}, issn = {0167-8094}, journal = {Order-A Journal on the Theory of Ordered Sets and its Applications}, title = {Algebraic Aspects of Relatively Pseudocomplemented Posets}, url = {https://doi.org/10.1007/s11083-019-09488-1}, volume = {37}, year = {2020} }
TY - JOUR ID - 1693381 AU - Chajda, Ivan - Langer, Helmut - Paseka, Jan PY - 2020 TI - Algebraic Aspects of Relatively Pseudocomplemented Posets JF - Order-A Journal on the Theory of Ordered Sets and its Applications VL - 37 IS - 1 SP - 1-29 EP - 1-29 PB - Springer SN - 01678094 KW - Relative pseudocomplementation KW - Poset KW - Hilbert algebra KW - Congruence KW - Convex poset KW - Dedekind-MacNeille completion KW - Glivenko equivalence KW - Category UR - https://doi.org/10.1007/s11083-019-09488-1 L2 - https://doi.org/10.1007/s11083-019-09488-1 N2 - In Chajda and Langer (Math. Bohem. 143, 89-97, 2018) the concept of relative pseudocomplementation was extended to posets. We introduce the concept of a congruence in a relatively pseudocomplemented poset within the framework of Hilbert algebras and we study under which conditions the quotient structure is a relatively pseudocomplemented poset again. This problem is solved e.g. for finite or linearly ordered posets. We characterize relative pseudocomplementation by means of so-called L-identities. We investigate the category of bounded relatively pseudocomplemented posets. Finally, we derive certain quadruples which characterize bounded Hilbert algebras and bounded relatively pseudocomplemented posets up to isomorphism using Glivenko equivalence and implicative semilattice envelope of Hilbert algebras. ER -
CHAJDA, Ivan, Helmut LANGER a Jan PASEKA. Algebraic Aspects of Relatively Pseudocomplemented Posets. \textit{Order-A Journal on the Theory of Ordered Sets and its Applications}. Dordrecht: Springer, 2020, roč.~37, č.~1, s.~1-29. ISSN~0167-8094. Dostupné z: https://dx.doi.org/10.1007/s11083-019-09488-1.
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